A particle of charge ` 1 mu C & ` mass `1 g` moving with a velocity of ` 4 m//s` is subjected to a uniform electric field of magnitude ` 300 V m` for ` 10 sec`. Then it's final speed cannot be :

Options

A. 0.5 m/s
B. 4 m/s
C. 3 m/s
D. 6 m/s

Answer

To solve the problem, we need to analyze the motion of a charged particle in a uniform electric field. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Charge of the particle, \( q = 1 \, \mu C = 1 \times 10^{-6} \, C \)
- Mass of the particle, \( m = 1 \, g = 1 \times 10^{-3} \, kg \)
- Initial velocity, \( u = 4 \, m/s \)
- Electric field strength, \( E = 300 \, V/m \)
- Time duration, \( t = 10 \, s \)

### Step 2: Calculate the force acting on the particle
The force \( F \) acting on the charge due to the electric field is given by:
\[ F = qE \]
Substituting the values:
\[ F = (1 \times 10^{-6} \, C)(300 \, V/m) = 3 \times 10^{-4} \, N \]

### Step 3: Calculate the acceleration of the particle
Using Newton's second law, \( F = ma \), we can find the acceleration \( a \):
\[ a = \frac{F}{m} = \frac{3 \times 10^{-4} \, N}{1 \times 10^{-3} \, kg} = 0.3 \, m/s^2 \]

### Step 4: Determine the final speed in two scenarios
1. **Acceleration in the direction of motion**:
- The final speed \( v \) can be calculated using the formula:
\[ v = u + at \]
Substituting the values:
\[ v = 4 \, m/s + (0.3 \, m/s^2)(10 \, s) = 4 + 3 = 7 \, m/s \]

2. **Acceleration opposite to the direction of motion**:
- The final speed \( v \) in this case is:
\[ v = u - at \]
Substituting the values:
\[ v = 4 \, m/s - (0.3 \, m/s^2)(10 \, s) = 4 - 3 = 1 \, m/s \]

### Step 5: Determine the range of possible final speeds
From the calculations, the final speed can vary between:
- Maximum speed: \( 7 \, m/s \)
- Minimum speed: \( 1 \, m/s \)

### Step 6: Identify which speed is not possible
The possible final speeds range from \( 1 \, m/s \) to \( 7 \, m/s \). Any speed outside this range is not possible. Therefore, if we consider a speed like \( 0.5 \, m/s \), it does not fall within the calculated range.

### Conclusion
The final speed of the particle cannot be \( 0.5 \, m/s \).